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Question 1181228: Each month ZV Corp (Zebra Vehicles where all paint jobs are striped) makes 230 A vehicles which get 10mpg,500 B vehicles which get 20mpg,and 70 C vehicles which get 40mpg. Unfortunately, the government sets a standard where companies must “average”30mpg[this is called a CAFElaw]. Any company that falls short of the 30mpg standard must pay a penalty. The penalty is calculated as $55times number of vehicles sold each month times the deficit in their average mpg from the 30mpg standard.
Compute ZV Corp’s monthly penalty if the government incorrectly uses (weighted) arithmetic mean to compute average mpg.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate ZV Corp's monthly penalty using the weighted arithmetic mean:
1. **Calculate the weighted average mpg:**
The weighted average mpg is calculated by multiplying each vehicle type's mpg by its proportion of total vehicles and then summing those results.
* Total vehicles: 230 (A) + 500 (B) + 70 (C) = 800 vehicles
* Weight of A vehicles: 230/800 = 0.2875
* Weight of B vehicles: 500/800 = 0.625
* Weight of C vehicles: 70/800 = 0.0875
Weighted average mpg = (0.2875 * 10) + (0.625 * 20) + (0.0875 * 40)
Weighted average mpg = 2.875 + 12.5 + 3.5
Weighted average mpg = 18.875 mpg
2. **Calculate the mpg deficit:**
Deficit = Standard mpg - Weighted average mpg
Deficit = 30 mpg - 18.875 mpg
Deficit = 11.125 mpg
3. **Calculate the total penalty:**
Penalty = $55 * Total vehicles * Deficit
Penalty = $55 * 800 * 11.125
Penalty = $489,500
Therefore, if the government incorrectly uses the weighted arithmetic mean, ZV Corp's monthly penalty would be $\boxed{489,500}$.
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